We developed a variance reduction method of Monte Carlo simulations as well as an approximation formula based on an asymptotic expansion approach for pricing bond options and swaptions in HJM framework. As a numerical example we applied the technique to a realistic two-factor model and confirmed...

This paper proposes a structural model to price credit risk of firms with short-term and long-term debts. This enables one to distinguish between default probabilities in the short run and in the long run, and to identify how the composition of debts affects credit risk. We endogenize the banks'...

This paper proposes a new three-factor model with stochastic mean reversions for commodity prices and derives the closed-form solution for the term structure of futures prices. It also examines the relation of our model with Schwartz(1997) type models that explicitly include interest rates and...

This paper proposes a structural model to price credit risk of firms with short-term and long-term debts. This enables one to distinguish between default probabilities in the short run and in the long run, and to identify how the composition of debts affects credit risk. We endogenize the banks'...

This paper proposes a new three-factor model with stochastic mean reversions for commodity prices and derives the closed-form solution for the term structure of futures prices. It also examines the relation of our model with Schwartz(1997) type models that explicitly include interest rates and...